Multiplying Fractions: Keeping the Skill in Context

I have found my students struggling to grasp the act of multiplying and dividing fractions conceptually. One suggestion would be to always keep it in context – I like to introduce and practice the skill by using word problems.

5th Grade TEKS related to Multiplication of Fractions[Supporting Standard] 5.3I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models

The progression

– #1 Multiplication of fractions1) Whole Number Multiplied by a Fraction (Combining Equal Groups of a Fractional Amount)
2) Fraction Multiplied by a Whole Number (Taking a Fractional Amount of a Whole Number)
3) Mix the two type of multiplication problems

The Break Down

Here are some ways I helped my students “break it down” when applying the skills to word problems1) Talk about the ACTION
– Combining (x)2) Draw a model or picture representation
– Helps students strengthen conceptual understanding
– Supports the TEKS that deal with REPRESENTING the multiplication and division of fractions using models
– Shows student thinking and helps students justify their thinking3) Answer the question in a complete sentence
– Forces students to reflect and makes sure they answered the initial question

Activate Prior Knowledge

What is multiplication? Combining equal groups.

The commutative property makes the answer correct regardless of the type of multiplication problem, right? Yes, but taking the time to teach students the two different types of problems really makes the difference in their conceptual understanding – which then has an impact on their ability to successfully solving word problems.

Two types of Multiplication problems

Whole Number Multiplied by a Fraction (Combining Equal Groups of a Fractional Amount)

Ms. Shim is running 2/3 of a mile every day. If she runs the same amount for 2 days, how many miles will she run in total?

Equation in words:We need to combine two equal groups of 2/3 to find the total number of miles she runs.

At first, I made my students merely write out the equation (example 2/3 x 2). However, I found that this didn’t help my students really dissect the word problem. What I found that helped was if I made my students write out the equation in their own words and identify the action.

Equation:2 x 2/3An extra step if deemed needed.

Model:

Area models and labeling is something I emphasize. This helps me see students thinking and students are able to use their models to prove their thinking.

Answer in a complete sentence: She will run a total of 1 and 1/3 of a mile.This helps the student reflect. They are forced to go back and make sure they answered the initial question.

Fraction Multiplied by a Whole Number (Taking a Fractional Amount of a Whole Number)

Ms. Shim baked 12 cookies and is planning to give them to her friends. However, 1/4 of those cookies were burnt. How many cookies were burnt?

This problem involves taking part of a whole number

The whole number is the total number of cookies Ms. Shim made.
The part that is being taken is the 1/4 of the burnt cookies.

Equation in words:There’s a total of 12 cookies and four equal groups. We need to find how many cookies are burnt in one group.

Total of 12 cookies // Split the cookies in 4 groups because the denominator shows us how many equal groups there are // See how many burnt cookies are in 1 of the groups because of the numerator.

Equation:1/4 x 12Model:

Answer in a complete sentence: There are 3 cookies that are burnt.

Stay tuned for a blog post that explains how I teach my students the division of fractions!